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A036234
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Number of primes <= n, if 1 is counted as a prime.
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17
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1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This sequence is the largest non-decreasing sequence a(n) such that a(Prime(n)-1) = n. - Tanya Khovanova (tanyakh(AT)yahoo.com), Jun 20 2007
a(n) = partial sums of A080339(n) [characteristic function of {1} union {primes}: 1 if n is 1 or a prime, else 0]. a(n) = A000720(n) + 1. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 23 2009]
Let G(n) be the graph whose vertices represent integers 1 through n, and where vertices a and b are adjacent iff gcd(a,b)>1. Then a(n) is the independence number of G(n). [From Aaron Dunigan AtLee (aaron(AT)duniganatlee.com), May 23 2009]
A036234(1)=1 ; A036234(n)= max[A061395(n), A061395(n-1)] - Jacques Alardet, Dec 28 2011
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MATHEMATICA
| Table[PrimePi[n] + 1, {n, 100}] - Tanya Khovanova (tanyakh(AT)yahoo.com), Jun 20 2007
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CROSSREFS
| Cf. A000720.
Cf. A080339, A000720. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 23 2009]
Sequence in context: A038567 A185195 A192512 * A061091 A196241 A086592
Adjacent sequences: A036231 A036232 A036233 * A036235 A036236 A036237
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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